Abstract

A granular flow is a two-component flow with an assembly of discrete solid particles dispersed in a fluid. Because of the similarity between the random motion of particles in a granular flow and the motion of molecules in a gas, the dense-gas kinetic theory has been broadly employed to analyze granular flows. However, most research only discusses aspects of momentum transport; three issues have received less attention: the diffusion process, the heat transfer problem, and the behavior of binary mixtures. The current research emphasizes these aspects.

A granular flow diffusion experiment was conducted in a vertical channel to investigate the effects that result in mixing of the material. The mean velocities, the longitudinal fluctuating velocities, and the mixing-layer thickness were measured. A simple analysis based on the diffusion equation shows that the thickness of the mixing layer increases with the square-root of downstream distance and depends on the magnitude of the velocity fluctuations relative to the mean velocity. The experimental velocity profiles were also compared with profiles calculated from theoretical analysis based on kinetic theory.

The analytical relations were developed for the flow-induced particle diffusivity and the thermal conductivity based on dense-gas kinetic theory. The two coefficients were found to increase with the square-root of the granular temperature, a term that quantifies the specific kinetic energy of the flow. The theoretical particle diffusivity was used to compare with the current experimental measurements involving the granular flow mixing layer. The analytical expression for the effective thermal conductivity was also compared with experimental measurements. The differences between the predictions and the measurements suggest limitations in some of the underlying kinetic-theory assumptions.

The constitutive relations were presented for a binary-mixture of granular materials as derived from the revised Enskog theory. The current research focuses on the process of granular thermal diffusion - a diffusion process resulting from the granular temperature gradient. A granular flow of binary-mixtures in an oscillatory no-flow system, in a sheared system, and in a vertical channel were examined, and indicated a complete segregation when granular thermal diffusion effect was sufficiently large.